Two-agent scheduling on bounded parallel-batching machines with an aging effect of job-position-dependent

This paper investigates a competitive two-agent parallel-batching scheduling problem with aging effect on parallel machines. The objective is to minimize the makespan of agent A with the constraint that the makespan of agent B is no more than a given threshold. Some key structural properties are first identified in two different cases, and based on these structural properties a novel decision tree of scheduling rules is constructed and a heuristic algorithm is designed. Then, an effective hybrid BF-VNS algorithm combining Bacterial Foraging (BF) with variable neighborhood search (VNS) is developed to tackle the studied problem. Computational experiments are conducted to evaluate the performance of the proposed hybrid algorithm and some other well-known algorithms. The experimental results indicate that the hybrid BF-VNS algorithm performs quite better than the compared algorithms.